A385479 - OEIS

A385479

a(n) is the cardinality of the union of the sets of divisors of sigma(k) for 1 <= k <= n.

1, 2, 4, 5, 6, 7, 8, 10, 11, 13, 13, 15, 15, 16, 16, 17, 17, 18, 20, 22, 24, 25, 25, 27, 27, 27, 28, 29, 29, 30, 30, 31, 32, 34, 34, 35, 37, 37, 37, 39, 39, 40, 43, 44, 46, 46, 46, 48, 49, 50, 50, 52, 52, 53, 53, 53, 54, 54, 54, 55, 55, 55, 57, 58, 58, 59, 62, 63

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Felix Huber, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = |Union_{k=1..n} divisors(sigma(k))|.

EXAMPLE

The divisors of sigma(1) = 1 are {1}, those of sigma(2) = 3 are {1, 3}, of sigma(3) = 4 are {1, 2, 4}, and of sigma(4) = 7 are {1, 7}. The union of these four sets is {1, 2, 3, 4, 7}, which has a cardinality of 5. Therefore, a(4) = 5.

MAPLE

with(NumberTheory):

A385479:=proc(n)

option remember;

local d, s;

if n=1 then

[{1}, 1]

else

d:=procname(n-1)[1];

s:=Divisors(sigma(n));

return [s union d, procname(n-1)[2]+nops(s minus d)]

fi;

end proc;

seq(A385467(n)[2], n=1..68);

MATHEMATICA

Module[{d = {}}, Table[Length[d = DeleteDuplicates[Join[d, Divisors[DivisorSigma[1, n]]]]], {n, 100}]] (* Paolo Xausa, Jul 07 2025 *)

PROG

(PARI) a(n) = my(s=Set()); for(k=1, n, s=setunion(s, divisors(sigma(k)))); #s; \\ Michel Marcus, Jul 01 2025

CROSSREFS

Partial sums of A385467.

Cf. A000005, A000203, A027750, A062068, A385478.

Sequence in context: A085302 A193928 A146215 * A086743 A285432 A039079

Adjacent sequences: A385476 A385477 A385478 * A385480 A385481 A385482

KEYWORD

nonn

AUTHOR

Felix Huber, Jul 01 2025

STATUS

approved